Thu 22 Nov 2007
Similarity Breeds Contentment
Posted by anaglyph under Mathematics, Philosophy, Science, Sound
[11] Comments
From time to time I get to musing on all manner of things here on The Cow, and today I bring you some thoughts about nature and self-similarity.
This morning at dawn I was lying half-awake listening to the song of a chirpy early-rising Turdus merula, better known as the Common Blackbird. The Blackbird was introduced to Australia, in Melbourne where I am now living, in the 1850s as part of the regrettable We-Wish-It-Was-More-Like-England makeover that the colonists were hell-bent on giving this completely un-Englandlike continent.
The Blackbird’s song is very pretty and very recognizable – listen to the end part of this sample:*
What I realized as I was listening though, was that the little guy† wasn’t just doing the same exact phrase over and over – there were little variations each and every time – just like he was improvising on his little blackbirdy theme. No two riffs were exactly alike.
This got me to speculating about another well-known natural phenomenon in which no two elements are exactly alike, but are very similar in structure and beauty and precision: the snowflake.
And so I began to wonder if the song of the Common Blackbird might in fact be the aural equivalent of the crystalline structure of the snowflake.‡
I don’t really know why I should have made that connection, but there you go. Put it down to my hypnopompic state if you like. But I leave you with this thought: self-similarity is rife in nature. It is embedded everywhere from the mathematics of fractals to the formation of snow crystals and the songs of birds. Its presence is felt in almost every natural process somehow or other. Think about it: it really does not need to be this way. All things considered, the natural world could be completely random. And yet order arises spontaneously everywhere it can.
The reasons for this remain a beautiful mystery.
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*This recording by Fred Van Gessel. I pinched it, so for my atonement I urge you to go buy his recording Bird Calls of the Greater Sydney Region from the Australian Museum Shop.
†It was most likely a male territorial song.
‡For a totally absorbing read, go visit this website dedicated to the fastidious, and one must say, obsessive, Wilson Bentley, a man who dedicated his life to the observation and photographic recording of snow crystals.
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The uniqueness of every single creation.
True of humans also,.
Thankfully, in some cases.
I love a good mystery :-)
Blackbird singing in the dead of night . .
If you have extra blackbirds, I hear they are really good in pie.
Reverend, obviously it is the work of our Lord Jesus Christ and God. DUH. I thought you knew better.
I dunno, Rev. Reading about snowflakes and listening to blackbirds? Maybe you need to get out more.
Meggie: Unique, and yet…
nursemyra: My own theory is that the butler did it.
Malach: Lucky I didn’t write that song. ‘Blackbird singing in the early hours of the morning’ doesn’t scan so good.
Colonel: I dunno. I prefer my pies to be silent…
jmf: Welcome back anonymous!!! Long time no hear. Oh… it’s you jmf. Sorry, case of mistaken identity.
Catalyst: I think the real problem here, Catalyst, is that I get out too much.
I was thinking of that exact same thought, or at least a sort of self-replicating thought when I was listening to my collection of Miles Davis’ more controversial (Jack Johnson, etc.) sessions.
The reason for the connection was that I was studying some minerals in the lab and it occured to me that while the size or color or even sometimes composition of mineral specimen are totally variable, the math is not. The angles are constant, even down to the molecular level. However, as the mineral crystalizes, and the system replicates itself geometrically, chaos creeps in, but the mineral is still recognizable, even with the addition of different cations.
Anyway, snowflakes are a mineral, so you already see how the same crystaline structure replicating leads to random (mostly) shapes, but similar forms. The interplay of John McLaughlin and Davis over repeating, even replicating, riffs is more or less the same idea. The same way people appreciate the repeated, but entropic, nature of minerals, they seem to appreciate the same sort of music.
Enter thoughts on human comprehension of the greater order, mystery, shadows on the cave wall, etc.
Then I realized I haven’t been part of a good jam session in a while. It made me sad.
Sorry about the long comment, just sort of hit a synaptic nerve.
Casey: I live for the long comment.
Especially when it’s from someone who totally gets it.
“hypnopompic”…..mmmm, new word!
One, hypnopompic is a wonderful word, and I hope to use it in conversation soon.
Two, I once spent half an hour listening to a bunch of crows, and they rarely repeated, and yet sometimes two or more would be cawing the same thing at the same time. I came to the conclusion that they were speaking a language I couldn’t understand, but that it all had to do with plots to take over the world. Or possibly they were just discussing the locations of the best dumpsters. Whichever. It certainly wasn’t random.
Blackbirds sound prettier than crows. But I figure they’d plot world domination, too, given half a chance.